Mathematics - Oral Examination


I think for this one [the oral exam]....what I did actually was practice asking my friends, questions, asking for the proofs, and what we can really come up with difficult questions ourselves . . . What helped was practicing orally and reading all.



I prefer the oral exams generally. I could’ve sat MA and MB as written exams and I would’ve been fine [. . . The oral exam] made the course more interesting and engaging because during the classes... you felt that you were forced to participate and engage.



I’m just thinking back to my experience in my internship where I had to explain complex sorts of mathematical concepts to clients, and you have to do it on the spot. And if they have any questions, you have to answer on the spot as well, there’s no such thing as ’Give me 10 minutes to think about it.’ You know, an oral exam really simulates a real-life experience . . .


External examiner-

I think if you have a good education as a mathematician you must be able to present mathematics to others, best in the traditional way on a traditional blackboard. And these are skills you really learn for life because whatever these people [the students] later do [...] they have to explain to their colleagues something [...] the oral examination is the best preparation for that because they will remember it.


Christoph Czichowsky (LSE),  Paola Iannone (Mathematics Education Centre, Loughborough University), Johannes Ruf (LSE).




We implemented a high-stake oral examination.  100% of the final grade for two year 3 financial mathematics modules was determined by oral assessment.

Target audience

3rd year undergraduate students who take one of the two modules MA313 (Introduction to Probability) or MA310 (Introduction to Financial Mathematics).


The two modules MA310 and MA313 are relatively small third-year courses with about 10 to 20 students each. MA313 is a prerequisite for MA310. Until 2017, both of the two modules were assessed by a written exam.  Due to the many benefits of oral assessment (see below), we changed the assessment to a 100% oral examination of 30 minutes length.

To prepare students, in each module we had mock exams with each student. In MA313, those mock exams were close in style to the final assessment: the student met the lecturer in a teaching room for 15 minutes where they were quizzed on the course content. In MA310, mock exams happened during class time. At the beginning of each class, one or two students who volunteered the week before were publicly quizzed. Both these mock exams were purely formative and did not contribute to the final mark.

We organized a room for three days in the second week of the summer term. We then scheduled the 18 students (11 of whom took both modules) for a total of 29 half-an-hour sessions. During these sessions, the assessment took place. At the end of each day, we ranked students and then assigned marks. Those grades counted for 100% of the students’ final mark.  All exams were filmed and the recordings were made available to the external examiner.

As Fields Medallist Martin Hairer puts it: “One of the most striking differences between the UK educational system and most of the other European educational systems is the importance given to oral examinations. This is quite surprising to many outsiders given the importance that communication skills have in many aspects of professional life.” While oral exams are not common in the UK, they are state-of-the-art to assess advanced mathematics courses at most European Universities. The idea of introducing oral exams at LSE was developed by Christoph during his assignment on course design for the PGCert. While closed-book written exams are “the golden standard” (Iannone and Simpson, 2015) in the UK, oral exams are better aligned with the higher intended learning outcomes of advanced mathematics in the spirit of Biggs’ constructive alignment in course design (Biggs, 1996). The advantages of oral assessment, as compared to the unseen written examination, can be summarised as follows (see also Joughin, 2010):

  • Oral examinations are suitable for testing understanding and critical evaluation of the main concepts and results, rather than just knowledge.
  • The assessor can observe what the students are doing and point them in the right direction: interaction allows for a more accurate assessment and therefore fosters deeper learning; in this way, oral exams also provide immediate student feedback.
  • A small gap in a student’s knowledge can stall the whole of a solution in a written examination, whereas the student can be guided past the gap in an oral examination.
  • Students learn to communicate mathematics verbally, a skill that enhances their employability and has been found in studies to be valued by students.

Since we all had good experiences with oral exams as students, it was a natural step for us to also try to introduce oral exams at LSE, where we were supported by many in our Department.


The LSE Teaching and Learning Centre provided us with a grant to do a study on the outcomes of the implementation of oral examination. Throughout the academic year, questionnaires were handed out to and interviews done with those students who agreed to take part in the study. The results were not shared with the two lecturers until all participants graduated. Additional data were collected. The results are currently being evaluated and will be summarized in one or more research articles.

Many, although not all, students changed the way they prepared for the oral exam. Instead of doing past exams and learning techniques by heart, they learned for understanding. Some of the students practiced for the oral exam by quizzing each other. We also noticed that students were more active in the lectures and exercise classes.

Next steps

As a department we are considering extending oral exams to other smaller year 3 courses. Oral exams might be also good format for resit exams.

A clear communication with the students is essential before the start of the module. Expectations need to be set out and the format of the oral exam also clearly set out. Indeed, LSE students do not usually have much experience of oral examinations, so they may feel anxious about them. The organization and preparations of the exam (room bookings, organization of cameras) should be done relatively early, best just when the exam timetabling is published.

Biggs, J., 1996. Enhancing teaching through constructive alignment. Higher Education, 32(3): 347-364.

Hairer, M. Oral examinations / presentations, Available at, last accessed on December 3rd, 2018

Iannone, Paola, and Adrian Simpson. Students' preferences in undergraduate mathematics assessment. Studies in Higher Education 40, no. 6 (2015): 1046-1067.

Joughin, Gordon. A short guide to oral assessment. Leeds Met Press in association with University of Wollongong, 2010.